Question: Simplify; express your answer in exponential form. Assume $p\neq 0, k\neq 0$. $\dfrac{{p^{2}k}}{{(p^{-4}k^{4})^{-2}}}$
Explanation: To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${p^{2}k = p^{2}k}$ On the left, we have ${p^{2}}$ to the exponent ${1}$ . Now ${2 \times 1 = 2}$ , so ${p^{2} = p^{2}}$ Apply the ideas above to simplify the equation. $\dfrac{{p^{2}k}}{{(p^{-4}k^{4})^{-2}}} = \dfrac{{p^{2}k}}{{p^{8}k^{-8}}}$ Break up the equation by variable and simplify. $\dfrac{{p^{2}k}}{{p^{8}k^{-8}}} = \dfrac{{p^{2}}}{{p^{8}}} \cdot \dfrac{{k}}{{k^{-8}}} = p^{{2} - {8}} \cdot k^{{1} - {(-8)}} = p^{-6}k^{9}$